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Lie Groups and Representation Theory
Seminar information archive ～04/24｜Next seminar｜Future seminars 04/25～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2021/07/06
17:00-18:00 Room #Online (Graduate School of Math. Sci. Bldg.)
Taito Tauchi (Kyushu University )
A counterexample to a Q-series analogue of Casselman's subrepresentation theorem (Japanese)
Taito Tauchi (Kyushu University )
A counterexample to a Q-series analogue of Casselman's subrepresentation theorem (Japanese)
[ Abstract ]
Let G be a real reductive Lie group, Q a parabolic subgroup of G, and π an irreducible admissible representation of G. We say that π belongs to Q-series if it occurs as a subquotient of some degenerate principal series representation induced from Q. Then, any irreducible admissible representation belongs to P-series by Harish-Chandra’s subquotient theorem, where P is a minimal parabolic subgroup of G. On the other hand, Casselman’s subrepresentation theorem implies any representation belonging to P-series can be realized as a
subrepresentation of some principal series representation induced from P. In this talk, we discuss a counterexample to a Q-series analogue of this subrepresentation theorem. More precisely, we show that there exists an irreducible admissible representation belonging to Q-series, which can not be realized as a subrepresentation of any degenerate
principal series representation induced from Q.
Let G be a real reductive Lie group, Q a parabolic subgroup of G, and π an irreducible admissible representation of G. We say that π belongs to Q-series if it occurs as a subquotient of some degenerate principal series representation induced from Q. Then, any irreducible admissible representation belongs to P-series by Harish-Chandra’s subquotient theorem, where P is a minimal parabolic subgroup of G. On the other hand, Casselman’s subrepresentation theorem implies any representation belonging to P-series can be realized as a
subrepresentation of some principal series representation induced from P. In this talk, we discuss a counterexample to a Q-series analogue of this subrepresentation theorem. More precisely, we show that there exists an irreducible admissible representation belonging to Q-series, which can not be realized as a subrepresentation of any degenerate
principal series representation induced from Q.
